A recent, systematic study of undirected networks found that cooperation will be disfavored, regardless of the benefit-to-cost ratio, for roughly one-third of network structures [1]}. Many of these structures even favor the evolution of spite [1]}. And yet we have found that, even for such networks, conversion of some bidirectional edges to uni-directional can rescue cooperation. An important implication is that directionality provides an alternative method of modifying population structure to promote cooperation — besides severing old ties and building new ones, as has been explored in the undirected setting [1]}, [4]}, [5]}. In particular, we have identified two specific structural motifs, triangular cycles for downstream behavior dispersal and in-in pairs for upstream dispersal, that efficiently guide structural modifications that favor the spread of cooperative behavior.
